Method to fabricate pre-patterned surfaces during manufacture of complex wrinkled structures

ABSTRACT

The pattern complexity and functional value of wrinkled structures can be substantially increased by fabricating the wrinkles on pre-patterned quasi-planar substrates instead of flat substrates. This disclosure presents the methods for fabricating pre-patterned polymeric surfaces that can be subsequently used as the substrates during manufacture of complex wrinkled structures. Pre-patterned substrates are generated by imprinting the pre-patterns onto the substrates during the curing process. Suitability for post-curing use in fabrication of wrinkles is ensured by (i) delayed imprinting that occurs close to but before the gelation point and (ii) gradual alignment of pre-patterns to the direction of stretch that is applied later during manufacture of wrinkled structures.

RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.14/669,925 filed on Mar. 26, 2015; this application also claims thebenefit of U.S. Provisional Application No. 61/970,434 filed on Mar. 26,2014. The entire contents of both of these applications are incorporatedherein by reference.

BACKGROUND OF THE INVENTION

This invention relates to the low-cost manufacture of a tunable physicaltopographic pattern and more particularly to the manufacture of microand nano scale hierarchical periodic wrinkle patterns that are generatedupon compression of supported thin films.

Micro and nano enabled devices have the potential to significantlyimpact diverse fields with direct societal benefits such as energy,water, health, and environment among others. These devices function byactively manipulating matter and/or energy on the micro/nano lengthscale and often rely on the structure-property relationship to achievethis manipulation. This active manipulation enables using micro/nanoenabled products in applications such as (i) fluidics based medicaldiagnostics, (ii) high-sensitivity sensing of toxic chemicals, and (iii)optoelectronics based chemical and biological sensing. As these devicesrely on the structure-property relationship, several differentproperties can be simultaneously controlled by incorporating differenttypes of structures on the same device. One of the techniques to achievethis is via fabrication of hierarchical structures. A hierarchicalstructure is one that comprises features on multiple length scales anddemonstrates “nested features”, i.e., a set of features built on top ofanother set of features. Each of these set of features may be used tocontrol a different material property. For example, large-scale featuresin a hierarchical structure may be used to direct/manipulate fluid flowwhereas small-scale features may be used to tune the localadhesion/stickiness. Thus, low-cost fabrication of hierarchicalmicro/nano structures is essential if one desires affordablemanufacturing of multi-function micro/nano enabled devices.

Current processes for fabricating micro/nano scale hierarchicalstructures are primarily limited in terms of the (i) cost andscalability of fabrication and (ii) tunability of hierarchy. At present,hierarchical micro/nano structures are fabricated via a combination oftwo or more substantially different fabrication processes. This leads tomanufacturing challenges in terms of throughput, cost, and/orscalability as one needs to satisfy the requirements for multipleprocesses. Additionally, it is infeasible to tune/modify the hierarchyafter the patterns have been fabricated. For example, it is currentlynot possible to deterministically switch a pattern acrossnon-hierarchical and hierarchical states or to change the relative“strength” of the individual patterns within the overall compositepattern. This inability to tune the hierarchy prevents one from applyinghierarchical structures to build tunable “smart” sensors and devices.Thus, there is a need to develop fabrication processes for scalable andaffordable manufacturing of tunable hierarchical micro/nano scalestructures. Herein, a scalable and affordable process to fabricatetunable hierarchical structures via a single fabrication process isdisclosed. This fabrication process was developed by performingwrinkling of pre-patterned surfaces wherein the pre-patterned surfacesare also fabricated via wrinkling.

Wrinkling of thin films is an affordable and scalable process forfabricating periodic sinusoidal patterns over large areas. Wrinkledpatterns are formed on supported thin films as a result ofbuckling-based instabilities and the mechanism is similar to Eulerbuckling of beams under compressive loads. A schematic of this processis illustrated in FIG. 1. Essential elements of a system thatdemonstrates wrinkle formation are: (i) a film 10 that is thin relativeto the base, (ii) mismatch in the elastic moduli of the film and thebase 12 with the film being stiffer than the base, and (iii) loadingconditions that generate in-plane compressive strain (ε) in the film. Insuch bilayer systems, the state of pure compression becomes unstablebeyond a critical strain and wrinkles are formed via periodic bending ofthe film/base. The period of wrinkles (λ) is determined by the competingdependence of strain energy on period in the film versus in the base.The amplitude (A) is determined by the amount of applied compressivestrain. Several different techniques have been developed in the past to(i) generate and join/bond the film to the base, (ii) generate modulimismatch, and (iii) apply uniaxial and biaxial strains to the film.During compression of flat/smooth films, one is limited to a singleperiod wrinkled pattern even with all of these different combinations oftechniques. Thus, to obtain hierarchical wrinkled patterns one muststart with non-flat film geometry.

Although fabrication of hierarchical wrinkled patterns has beendemonstrated in the past, current techniques for wrinkling have majorlimitations that prevent one from using these techniques in amanufacturing environment. These limitations are: (i) inability toaccurately predict the resulting pattern for a given set of processparameters and (ii) inability to perform inverse pattern design; i.e.,inability to predictively design and fabricate the desired hierarchicalpatterns by combining several patterns. Thus, using current techniquesone can fabricate some form of hierarchical wrinkles but not the desiredtargeted hierarchical pattern. This makes it impossible to use thecurrent techniques to (i) deterministically switch between hierarchicaland non-hierarchical states and (ii) predictively tune the relativestrength of the individual periodicities in the composite pattern.

Herein, a technique to deterministically tune the hierarchy of awrinkled surface is disclosed. The technique is based on the discoverythat the hierarchical form during compression of a non-flat bilayeremerges with increase in the compressive strain. This emergencephenomenon has been exploited here to design and fabricate wrinkledsurfaces with tunable hierarchy wherein the hierarchical form is tunedvia the applied compressive strain. A schematic representation ofemergence of hierarchy with compression is illustrated in FIG. 2. Thisdisclosure presents: (i) the process scheme for fabricating hierarchicalpatterns 22 from wrinkling of pre-patterned surfaces 16, (ii) the toolsthat enable controlling the parameters during the fabrication process,and (iii) model-driven design of such bilayer systems that demonstratetunable hierarchy. In combination, these tools and techniques enable oneto (i) predictively design and fabricate hierarchical patterns at1/10^(th) of the cost of the existing processes and (ii)deterministically tune the hierarchical form.

SUMMARY OF THE INVENTION

The process of generating tunable hierarchical wrinkle patterns consistsof the following steps: (1) generating the wrinkled pre-pattern viacompression of a polymer bilayer comprising a thin hard film 24 on topof a soft compliant base 25, (2) transferring this pre-pattern geometryonto a base layer 26 via imprinting, (3) generating a pre-patternedbilayer by depositing a thin film 16 on top of the patterned base 28,and (4) performing compression of this patterned bilayer. A schematic ofthe process is illustrated in FIGS. 3(a), 3(b), and 3(c). During step(1), 1-D wrinkle patterns are obtained upon uniaxial compression viaperiodic bending of the bilayer surface. The period and amplitude of thepre-pattern can be tuned by controlling the thickness of the hard thinfilm, material properties of the bilayer, and the applied compressivestrain. The period and amplitude of the emerging wrinkles can also betuned by controlling these parameters during steps (3) and (4). As theseparameters can be independently tuned between steps (1), (3) and (4), avariety of different hierarchical wrinkle patterns can be obtained bycombining the two patterns. Upon compression of the pre-patternedbilayer during step (4), one observes that first the pre-patterned mode20 persists with a growth in amplitude and then the mode transitionsover to a hierarchical pattern 22 beyond a threshold compression. Thepatterns are reversible between the pre-pattern 20 and the hierarchicalpattern 22 with reduced/increased compression around this threshold.Thus, tunable hierarchical patterns are be obtained by controlling thecompression during the final step. These patterns find applications inthe fabrication of tunable optical sensors and tunable microfluidiccircuits among others.

To be able to satisfactorily implement the process scheme describedabove, one requires tools that would enable controlling the processparameters during steps (1)-(4). These tools must: (i) control theapplied compressive strains during steps (1) and (4), (ii) control theimprinting process for accurate pre-pattern transfer during step (2) and(iii) accurately align the pre-patterns to the direction of subsequentloading during step (4). The biaxial tensile stage that is used forcontrolling the compressive strains has been disclosed elsewhere in U.S.patent application Ser. No. 14/590,448 titled “Biaxial Tensile Stage forFabricating and Tuning Wrinkles”. Herein, the tools and techniques forcontrolling the imprinting and alignment processes are disclosed. Awell-controlled imprinting process is achieved by performing delayedimprinting, i.e., by imprinting the pre-pattern onto the base materialwhile the base material is partially cured. Accurate alignment ofpre-pattern to loading direction is achieved by a gradual alignmentscheme. In this scheme, surface-to-edge alignment is first achieved viaalignment marks and then conformal surface-to-surface alignment isachieved via gradual engagement.

In addition to the process scheme and the tools, one must carefullydesign the pre-patterned bilayer systems if deterministic tunability ofhierarchy is desired. This is necessary to ensure that the transition ofthe pre-pattern into the hierarchical mode occurs at a practicallyfeasible compressive strain. Thus, not all possible combinations ofpre-patterns and process parameters will result in practical tunablesystems. To select the “right” set of process parameters, an analyticalphysics-based model of the process has been developed. This modelpredicts the critical strain for pre-pattern to hierarchy transition andguides the design of tunable bilayer systems. Herein, the set of processparameters that deterministically demonstrate tunability of hierarchy isdisclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1(a) and 1(b) are schematic illustration of wrinkle formationduring compression of a flat non-patterned bilayer system.

FIG. 2 is a schematic illustration of the phenomenon of emergence ofhierarchy during compression of pre-patterned bilayers.

FIGS. 3(a), 3(b), and 3(c) are illustration of the process scheme forfabricating tunable hierarchical wrinkles wherein the pre-pattern isalso fabricated via wrinkling FIG. 3(a) illustrates generation ofpre-pattern. FIG. 3(b) illustrates imprinting of pre-pattern andgeneration of pre-patterned bilayer. FIG. 3(c) illustrates thegeneration of hierarchical wrinkles via compression of pre-patternedbilayer.

FIGS. 4(a), 4(b), 4(c), and 4(d) are schematic illustration of theprocess of wrinkle fabrication via a prestretch based film compressiontechnique. FIG. 4(a) illustrates stretching of PDMS base. FIG. 4(b)illustrates plasma oxidation. FIG. 4(c) illustrates release ofprestretch. FIG. 4(d) illustrates the resulting wrinkle pattern.

FIGS. 5(a) and 5(b) are top and front views of a PDMS coupon that isuniaxially stretched.

FIG. 6(a) is a perspective view of the mold that is used for casting andcuring of PDMS films.

FIG. 6(b) is a cross-sectional view of the mold.

FIGS. 7(a) and 7(b) are schematic illustrations of the gradual alignmentand imprinting process.

FIGS. 8(a) and 8(b) are images of hierarchical wrinkled patterns thatwere fabricated via compression of pre-patterned bilayers wherein thepre-patterns were also fabricated via wrinkling FIG. 8(a) is an atomicforce microscopy image and FIG. 8(b) is an optical image.

FIG. 9 is an illustration of the dependence of the critical amplituderatio on the ratio of pre-pattern and natural periods.

DESCRIPTION OF THE PREFERRED EMBODIMENT

A hierarchical wrinkle pattern is one that comprises more than onespatial frequency, i.e., hierarchical wrinkle patterns demonstrateperiodic sinusoidal patterns of one period built on top of patterns ofanother period. In general, hierarchical patterns may demonstratehierarchy on several length scales, i.e. patterns with several differentperiods. In the preferred embodiment, fabrication of tunablehierarchical wrinkle patterns with two spatial periods is presented.

Tunable hierarchical wrinkle patterns are generated by performing aseries of two wrinkle-patterning operations with an intermediateimprinting pattern transfer process between the two steps. This schemeis illustrated in FIGS. 3(a), 3(b), and 3(c). In the firstwrinkle-patterning step one starts with a flat non-patterned bilayersystem, whereas in the last wrinkle-patterning step one starts with apre-patterned non-flat bilayer surface. Herein, the process forwrinkling of non-patterned flat bilayer systems via compression ispresented first and then the process of pattern transfer via imprintingis presented. The final step of wrinkle formation via compression ofpre-patterned bilayer is identical to the first wrinkle formation step.

A schematic of wrinkle pattern formation is depicted in FIG. 1. Toenable the fabrication of wrinkle patterns, one must solve thesesub-problems: (i) fabrication of a bilayer system with the desiredmaterial properties and geometry and (ii) compression of the top stifffilm.

Stretchable bilayers with large stiffness ratio can be fabricated byattaching or growing a thin stiff film 10 on top of a thick elastomericbase 12. For example, exposing a polydimethylsiloxane (PDMS) film to airor oxygen plasma leads to the formation of a thin glassy layer on top ofthe exposed PDMS surface via oxidation. Alternatively, a metallic orpolymeric thin film may be deposited on top of PDMS to obtain thedesired bilayer. The top layer thickness can be tuned by controlling theduration of plasma oxidation or the deposition process; whereas thestiffness ratio may be tuned by selecting the appropriate top/bottommaterials. In the preferred embodiment of the tunable patterns, bothplasma oxidation and metal/polymer film deposition techniques are usedto generate a stiff thin film on top of an elastomeric PDMS layer.

Compression of the top film can be achieved by either directlycompressing the bilayer or by generating a residual compressive strainin the top layer. As direct compression requires sustained loading tomaintain the wrinkles, residual compression is often the preferredscheme. During mechanical loading, residual compression is generated byfirst stretching the PDMS base and then attaching/growing the stiff filmon top of this pre-stretched base layer. On releasing the prestretch inthe PDMS, the top layer undergoes compression that leads to formation ofwrinkles. In the preferred embodiment of the pre-patterned bilayer, theprestretch is selected to be sufficiently high so that the transitioncompressive strain can be achieved during release of the prestretch.

The steps of the wrinkle fabrication process are illustrated in FIGS.4(a), 4(b), 4(c), and 4(d). The steps are (i) fabricating the base PDMSfilm 12, (ii) clamping the PDMS film in a tensile stage, (iii) extensionof the PDMS film, (iv) plasma oxidation of the stretched PDMS film ordeposition of metallic/polymeric thin film 10, and (v) release of theprestretch in the PDMS film. The base PDMS films were fabricated bycasting and thermally curing the commercially available Sylgard 184two-part silicone elastomer mixture in a ratio of 1 part curing agent to12 parts resin by weight. Rectangular coupons with a stretched length of37.5 mm, a clamped width of 20 mm, and a thickness of 1.9-2.2 mm werecut of the cast PDMS films. The film is illustrated in FIGS. 5(a) and5(b). To align the edges of the PDMS coupon 30 to the stretchingdirection, alignment features 32 were generated on the bottom surfaces33 of the films by incorporating them directly into the molds used forcuring. The edge 31 corresponding to these alignment marks is alignedperpendicular to the uniaxial stretch direction. These alignmentfeatures (i) ensure that the length of the stretched section isaccurately known during stretching and (ii) act as reference featuresfor alignment of the pre-patterns to the direction of stretching duringthe final wrinkling step.

The mold geometry is illustrated in FIGS. 6(a) and 6(b). The moldconsists of a cylindrical casting reservoir 38 that is 150 mm indiameter and has a nominal height of 2 mm. The casting reservoir issurrounded by an overflow reservoir 40 that holds any excess PDMS thatoverflows from the casting reservoir. This feature ensures that themaximum thickness of the PDMS films is limited to the height of thecasting reservoir. Films below this thickness may be fabricated bycontrolling the amount of pre-cured PDMS that is poured into the castingreservoir. Variations in thickness across the casting surface can bereduced by holding the mold surface level with respect to thegravitational field. For example, this may be achieved by performing thethermal curing operation on a hot plate that is itself kept on top of anoptical table. To ensure that featureless flat films are available forpatterning, only the top surface of the films is used for patterningwrinkles. The stretched length of the films is held uniform acrossdifferent samples by incorporating alignment features 34 into the molds.These mold features ensure that each PDMS coupon 30 has wellcharacterized alignment features built into it during the casting/curingprocess. The coupons can be cut out of the cast PDMS films by tracingout the outline 36 of the coupons.

During the first step of wrinkle formation on flat bilayers, the fullprestretch in the bilayer is released to generate the wrinkles that areused as the pre-pattern for the subsequent steps. During the last stepof wrinkle formation on pre-patterned bilayers, the prestretch ispartially released to tune the resultant hierarchical pattern.

The pre-patterned bilayers are fabricated on PDMS by using the wrinkledsurfaces as the molds/templates to generate the top surface of the PDMScasts. The curing process for fabrication of the pre-patterned base issame as that for the first wrinkling step presented above with theadditional step of imprinting the pre-pattern onto the PDMS materialduring curing. Imprinting is performed by “gently” placing thepre-patterned coupon on top of the exposed surface of the curing PDMSwhile taking care that the patterned surface 44 is oriented toward thecuring material 42. The imprinting process is illustrated in FIGS. 7(a)and 7(b).

A well-controlled imprinting process is essential to fabricate thedesired hierarchical patterns by ensuring accurate pre-patternreplication. Factors during imprinting that influence patternreplication are (i) contact force, (ii) uniformity of contact withminimum bubbles/gaps, and (iii) alignment of pre-patterns to thedirection of subsequent stretching. To ensure a well-controlledimprinting process, a protocol was developed. This protocol is listed inTable 1.

TABLE 1 Protocol for imprinting pre-patterns on PDMS # Step Protocol 1Mixing of two-part PDMS (resin + curing agent) with curing ratio of 1 r= 12 or r = 15 part curing agent for ‘r’ part resin; r ∈ [6, 15] 2Degassing of the two part mixture under vacuum pressure P_(d) for t_(d)P_(d) <= −28.5 inHg, t_(d) = 20 minutes minutes 3 Pouring two partmixture onto aluminum mold. The mold is held at T_(L) = 65° C. constanttemperature T_(L) using a hot plate 4 Low temperature curing up togelation point: Mold held at constant T_(L) = 65° C., t_(l) = 20 mintemperature T_(L) for t_(l) minutes 5 Imprinting pre-pattern onto thetop surface of PDMS mold t_(i) minutes after 6 min < t_(i) < 8 min startof curing 6 High temperature curing: increasing mold temperature toT_(H) after t_(l) T_(H) = 165° C., t_(h) = 15 min minutes of pouring andholding this temperature for t_(h) minutes. 7 Taking mold off the heaterand then placing it on aluminum thermal sink t_(s) = 10 min that ismaintained at room temperature for at least t_(s) minutes

In the presence of insufficient contact force, PDMS does not flow intothe pre-pattern; whereas high contact force leads to excess flow of PDMSunder the pre-pattern and a thinner-than-desired casting. Thesensitivity of flow to contact force decreases as curing proceeds due tothe increase in viscosity of PDMS. Therefore, delayed imprinting isperformed, i.e., imprinting close to, but before, the gelation pointinstead of at the beginning of the curing process. One must be carefulnot to cross the gelation point as the phase change at this pointprevents pattern replication.

To ensure uniform contact and to align the pre-patterns along thestretch direction, a gradual imprinting/alignment scheme was developed.This scheme is illustrated in FIGS. 7(a) and 7(b). Steps of this schemeare: (i) in-plane alignment of one of the edges 46 of the pre-patternedbilayer coupon to the alignment features 34 that are pre-fabricated onthe PDMS mold, (ii) bringing the aligned edge into contact with thecuring material, and (iii) gradually bringing the rest of thepre-pattern coupon into contact with the curing material. During gradualcontact, alignment is maintained due to the no-slip condition thatexists along the initial contact edge 46; uniformity of the contact canbe verified by visual inspection of the moving contact meniscus.

The process schemes and techniques described above enable one tofabricate wrinkled patterns via compression of pre-patterned bilayersbut are not sufficient when deterministically tunable hierarchicalpatterns are desired. For deterministic tunability, in addition to theprocess schemes and techniques one must also select the “right” set ofprocess parameters to design the bilayers. This set of “right”parameters is presented below.

The geometric parameters that are relevant to predictive design oftunable hierarchical wrinkles are: (i) the period (λ_(p)) of thepre-pattern, (ii) the amplitude of the pre-pattern (A_(p)), (iii) theperiod of the natural pattern (λ_(n)), and (iv) the amplitude of thenatural pattern (A_(n)). The natural pattern is the hypothetical patternthat would have been observed for an un-patterned flat bilayer that hasthe same material properties as the pre-patterned bilayer and iscompressed by the same amount. During design and prediction, the effectof material properties and compression is indirectly accounted for bythe natural period and amplitude; whereas the pre-pattern accounts forthe geometric effect. As the period and amplitude of the pre-patternsand natural patterns can be independently tuned, different types ofhierarchical patterns is feasible.

As the pre-patterns are fabricated via wrinkling, only a limited set ofpre-patterns are available. For uniaxial stretching, this set comprises1-D sinusoidal periodic patterns over a finite range of period (λ_(p))and amplitude (A_(p)). The feasible range of period and amplitude can beobtained from the fabrication constraints. Fabrication constraints arisedue practical limitations such as resolution of vision system,overheating during plasma oxidation or metal deposition, andfailure/tearing of PDMS during stretching. During fabrication ofwrinkles, period is controlled via the exposure time during plasmaoxidation and amplitude is controlled via stretching of PDMS.Additionally, both period and amplitude may be tuned over a small rangeby tuning the PDMS curing ratio, i.e., by tuning the Young's modulus ofPDMS. Thus, fabrication constraints can be linked to the feasible rangeof period and amplitude by quantifying the feasible range of (i) PDMSstretching (c), (ii) exposure time during plasma oxidation (t_(e)), and(iii) Young's modulus of PDMS. Out of these available pre-patterns andnatural patterns, only a subset would lead to tunable hierarchicalpatterns. To determine that set, an analytical model of the process wasdeveloped.

Hierarchical patterns are formed as result of the competition andcombination of two distinct modes of the wrinkled system. These twomodes are (i) pre-pattern that is imprinted onto the bilayer and (ii)natural pattern of the corresponding flat bilayer system. The naturalpattern of the flat bilayer system is determined by the thickness of thetop film, mechanical properties of the bilayer, and the applied strain.The contribution of each of these modes to the overall mode shape isdetermined by the applied compression. Below a critical thresholdcompressive strain, the pre-pattern mode is energetically favorable.Thus, during initial compression of the pre-patterned bilayer anon-hierarchical single period mode is observed. As the compression isincreased, the natural mode becomes energetically favorable. Thus, acombination of the pre-pattern and the natural mode is observed duringsubsequent compression. The critical compression threshold can bepredicted in terms of the pre-pattern and the natural pattern of thebilayer.

Pre-patterning a bilayer system changes the wrinkling process in twoways: (i) pre-patterning the surface provides a lower energy pathway tobending deformation as compared to the case of a flat surface, (ii)pre-patterning with a period that is not the natural period of the flatsystem leads to an energy penalty. The energy penalty arises as thenatural period of the flat system (by definition) is the lowest energymode for a flat system. Thus, the first effect causes the pre-patternedmode to have a lower energy whereas the second effect causes it to havea higher energy. The energy penalty remains independent of the appliedcompression; however, the energy advantage decreases with compression.Thus, beyond a critical threshold the pre-patterned mode becomesenergetically unfavorable. Beyond that compression, the natural modeemerges in addition to the pre-patterned mode. This results in theformation of a complex hierarchical mode. Examples of fabricatedhierarchical wrinkle patterns are shown in FIGS. 8(a) and 8(b).

A model of the process has been developed that captures the essentialphysics discussed above. The pre-pattern is quantified in terms of thepre-pattern period (λ_(p)) and the amplitude (A_(p)); similarly, thenatural pattern is characterized by the natural period (λ_(n)) and theamplitude (A_(n)). These parameters are represented in terms of thenon-dimensional parameters as: m=(λ_(p)/λ_(n)) and n=(A_(p)/A_(n)). Thenatural amplitude can be represented in terms of the applied compression(ε) as: A_(n)=(λ_(n)/π)ε^(0.5). The natural period of the system isindependent of the applied compression and depends only on the top filmthickness and the material properties of the pre-patterned bilayer.

The energy advantage due to pre-patterning is given by:(E_(p,n)/E_(n))=1−2[{η(1+η)}^(0.5)−η]. Here, E_(p,n) is the energy of apre-patterned bilayer with the same period as the natural period, E_(n)is the energy of the hypothetical flat bilayer, and η=n²/m². The energypenalty due to non-natural mode is given by:(E_(p,p)/E_(p,n))={(1+2m³)/(3m²)}. Here, E_(p,p) is the energy of apre-patterned bilayer with a pre-pattern period that is different fromthe natural period. The critical compression is achieved whenE_(p,p)=E_(n). Thus, the critical condition is given by:n_(c)=|1+2m³−3m²|/{12(1+2m³)}^(0.5). Here, n_(c) is the criticalamplitude ratio and |•| is the absolute value operator.

When the compressive strain in a pre-patterned bilayer is increased, theamplitude ratio increases. At the onset of compression, the amplituderatio ‘n’ is close to infinity as the amplitude of the natural period iszero. With increasing compressive strain, the natural amplitude of thehypothetical equivalent flat bilayer increases along with a decrease inthe amplitude ratio ‘n’. As long as the amplitude ratio remains higherthan the critical amplitude ratio ‘n_(c)’, only the single-periodpre-pattern exists. Physically, this manifests as an increase in theamplitude of the pre-patterned mode. With further compression,hierarchical patterns emerge when the amplitude ratio ‘n’ falls belowthe critical amplitude ratio ‘n_(c)’. This critical ratio is illustratedin FIG. 9 and depends only on the period ratio ‘m’. As this condition isindependent of the material properties, it is applicable to allcombinations of bilayer materials. The corresponding criticalcompressive strain is given as: ε_(t)={π(A_(p)/λ_(p))(m/n_(c))}².

When tunable hierarchical systems are desired, one must select theprocess parameters such that (i) the observed amplitude ratio is closeto the critical amplitude ratio ‘n_(c)’ and (ii) the prestretch in thepre-patterned bilayer is sufficiently high so that the amplitude ratiocan cross over the critical value upon full prestretch release. Theperiod ratio must be selected based on the desired application. Forexample, if a tunable optical sensor in the visible spectrum is desired,then one may select the pre-pattern as λ_(p)=700 nm and A_(p)=15 nm andthe period ratio ‘m’ as 2. The corresponding critical amplitude ratio isn_(c)=0.35. Thus, the prestretch in the pre-patterned bilayer must be atleast 14.8% to achieve hierarchical patterns. If a prestretch below thisvalue is applied then hierarchical patterns cannot be obtained even uponfull prestretch release; instead, one would observe an increase in thepre-pattern amplitude.

Another application of tunable hierarchical patterns is a tunablemicrofluidic channel wherein the pre-pattern is used as a channel forfluid flow and the hierarchical pattern is used as small-scale featuresthat control the surface roughness of the channels. In this application,one may select the pre-pattern as λ_(p)=5 um and A_(p)=500 nm and theperiod ratio ‘m’ as 10. The corresponding critical amplitude ratio isn_(c)=10.98. Thus, the prestretch in the pre-patterned bilayer must beat least 8.2% to achieve hierarchical patterns. When the prestretch inthe pre-patterned bilayer is not released, a smooth channel is obtained.Upon release of the prestretch beyond 8.2%, a rough surface is observed.This rough surface results due to the emergence of the hierarchicalwrinkles. The surface roughness of the channels can be tuned by furtherreleasing the prestretch.

The process schemes, techniques, and the bilayer design disclosed hereenable one to fabricate hierarchical wrinkled patterns wherein thehierarchy can be deterministically tuned via compression.

It is recognized that modifications and variations of the presentinvention will be apparent to those of ordinary skill in the art and itis intended that all such modifications and variations be includedwithin the scope of the appended claims.

In one variation, the pre-patterns may be fabricated by a process otherthan wrinkling. In such a scheme, the manufacturing advantages of usinga single fabrication process are lost. However, such a scheme may benecessary when pre-patterns are desired outside the feasible range ofpre-patterns that can be fabricated via wrinkling. For example,pre-patterns may be fabricated via an alternate process when largeamplitudes are desired. Even in such a scenario, the subsequent steps ofpre-pattern imprinting and compression of pre-patterned bilayers can beused to fabricate tunable hierarchical patterns.

In another variation, biaxial strains can be applied during pre-patterngeneration via wrinkling to generate 2-D periodic patterns. Imprintingthis pre-pattern and subsequent compression of the bilayer would lead tothe generation of an asymmetrical complex hierarchical pattern.

In another variation, biaxial strain may be applied during compressionof the pre-patterned bilayer with a uniaxially generated pre-pattern.This scheme would also lead to generation of an asymmetrical complexhierarchical pattern.

In another variation, the pre-pattern that is generated via uniaxialcompression may be aligned at a non-zero angle to the direction ofuniaxial prestretch in the pre-patterned bilayer. Alignment marks on thePDMS mold can be used to accurately align the pre-pattern at an angle tothe prestretch direction. This scheme would also lead to the generationof asymmetrical complex hierarchical patterns.

What is claimed is:
 1. A method to fabricate a pre-patterned base substrate by replicating a patterned surface, comprising: providing a coupon with a patterned surface, wherein the coupon has alignment features; providing a thermally curing base material, wherein the base material undergoes a liquid-to-solid phase transition during curing; providing a mold for curing the base material, wherein the mold surface has alignment features that correspond to a direction of stretch; heating the base material to a temperature below a threshold value to initiate the first thermal curing cycle, wherein the viscosity of the base material increases with time but the base material does not undergo a liquid-to-solid phase transition by the end of the first thermal cycle; aligning the patterned surface to the direction of stretch by locating the alignment features on the coupon with respect to the alignment features on the mold, wherein the patterned surface is not yet in contact with the base material; partially placing the coupon with the patterned surface on top of the base material, wherein only one edge of the coupon makes contact with the base material; releasing the coupon with the patterned surface on top of the base material, wherein the first-contact edge does not slip across the surface of the base material and the patterned surface makes contact with the base material, thereby leading to conformal contact between the patterned surface and the top surface of the base material before the end of the first thermal curing cycle; further heating the base material to a temperature below a threshold value to initiate the second thermal curing cycle, wherein the base material undergoes a liquid-to-solid phase transition; separating the coupon with the patterned surface from the base material after the onset of phase transition, thereby replicating the patterned surface onto the base material and generating a pre-patterned base substrate; and stretching the pre-patterned base substrate in a direction of stretch.
 2. The method of claim 1, wherein the patterned surface comprises wrinkled periodic patterns.
 3. The method of claim 1, wherein the temperature threshold for the first and second thermal curing cycles are identical.
 4. The method of claim 1, wherein the temperature threshold for the second thermal curing cycle is higher than the temperature threshold for the first thermal curing cycle.
 5. The method of claim 1, wherein the thermally curing material is polydimethylsiloxane.
 6. The method of claim 1, wherein the temperature threshold for the first thermal curing cycle lies in the range of 60-70 degree Celsius.
 7. The method of claim 1, wherein the temperature threshold for the second thermal curing cycle lies in the range of 135-170 degree Celsius.
 8. The method of claim 1, wherein conformal contact between the patterned surface and the base material is achieved within 6-8 minutes after the initiation of the first thermal curing cycle.
 9. The method of claim 1, wherein an external force is applied on the coupon with the patterned surface during its contact with the base material, thereby pressing the pre-patterned surface against the base material.
 10. The method of claim 1, wherein the coupon with the patterned surface is separated from the base material before the end of the second thermal curing cycle.
 11. A method to fabricate a pre-patterned base substrate by replicating a patterned surface, comprising: providing a coupon with a patterned surface; providing a thermally curing base material, wherein the base material undergoes a liquid-to-solid phase transition during curing; providing a mold for curing the base material; heating the base material to a temperature below a threshold value to initiate the first thermal curing cycle, wherein the viscosity of the base material increases with time but the base material does not undergo a liquid-to-solid phase transition by the end of the first thermal cycle; partially placing the coupon with the patterned surface on top of the base material, wherein only one edge of the coupon makes contact with the base material; releasing the patterned surface on top of the base material, wherein the first-contact edge does not slip across the surface of the base material and the patterned surface makes contact with the base material, thereby leading to conformal contact between the patterned surface and the top surface of the base material before the end of the first thermal curing cycle; further heating the base material to a temperature below a threshold value to initiate the second thermal curing cycle, wherein the base material undergoes a liquid-to-solid phase transition; separating the coupon with the patterned surface from the base material after the onset of phase transition, thereby replicating the patterned surface onto the base material and generating a pre-patterned base substrate; and stretching the pre-patterned base substrate in a direction of stretch.
 12. The method of claim 11, wherein the patterned surface comprises wrinkled periodic patterns.
 13. The method of claim 11, wherein the temperature threshold for the first and second thermal curing cycle are identical.
 14. The method of claim 11, wherein the temperature threshold for the second thermal curing cycle is higher than the temperature threshold for the first thermal curing cycle.
 15. The method of claim 11, wherein an external force is applied on the coupon with the patterned surface during its contact with the base material, thereby pressing the patterned surface against the base material.
 16. A method to fabricate a pre-patterned base substrate by replicating a patterned surface, comprising: providing a coupon with a patterned surface, wherein the coupon has alignment features; providing a thermally curing base material, wherein the base material undergoes a liquid-to-solid phase transition during curing; providing a mold for curing the base material, wherein the mold surface has alignment features that correspond to a direction of stretch; heating the base material to a temperature below a threshold value to initiate the first thermal curing cycle, wherein the viscosity of the base material increases with time but the base material does not undergo a liquid-to-solid phase transition by the end of the first thermal cycle; aligning the coupon with the patterned surface by locating the alignment features on the coupon with respect to the alignment features on the mold, wherein the patterned surface is not yet in contact with the base material; placing the coupon with the patterned surface on top of the base material before the end of the first thermal curing cycle; further heating the base material to a temperature below a threshold value to initiate the second thermal curing cycle, wherein the base material undergoes a liquid-to-solid phase transition; separating the coupon with the patterned surface from the base material after the onset of phase transition, thereby replicating the patterned surface onto the base material and generating a pre-patterned base substrate Stretching the pre-patterned base substrate in the direction of stretch.
 17. The method of claim 16, wherein the patterned surface comprises wrinkled periodic patterns.
 18. The method of claim 16, wherein the temperature threshold for the first and second thermal curing cycle are identical.
 19. The method of claim 16, wherein the temperature threshold for the second thermal curing cycle is higher than the temperature threshold for the first thermal curing cycle.
 20. The method of claim 16, wherein an external force is applied on the coupon with the patterned surface during its contact with the base material, thereby pressing the patterned surface against the base material. 